// Copyright (c) 2005  Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.

// Basic JavaScript BN library - subset useful for RSA encryption.

// Bits per digit
var dbits;

// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = (canary & 0xffffff) == 0xefcafe;

// (public) Constructor
function BigInteger(a, b, c) {
  if (a != null) if ("number" == typeof a) this.fromNumber(a, b, c);else if (b == null && "string" != typeof a) this.fromString(a, 256);else this.fromString(a, b);
}

// return new, unset BigInteger
function nbi() {
  return new BigInteger(null);
}

// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.

// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i, x, w, j, c, n) {
  while (--n >= 0) {
    var v = x * this[i++] + w[j] + c;
    c = Math.floor(v / 0x4000000);
    w[j++] = v & 0x3ffffff;
  }
  return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i, x, w, j, c, n) {
  var xl = x & 0x7fff,
      xh = x >> 15;
  while (--n >= 0) {
    var l = this[i] & 0x7fff;
    var h = this[i++] >> 15;
    var m = xh * l + h * xl;
    l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff);
    c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);
    w[j++] = l & 0x3fffffff;
  }
  return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i, x, w, j, c, n) {
  var xl = x & 0x3fff,
      xh = x >> 14;
  while (--n >= 0) {
    var l = this[i] & 0x3fff;
    var h = this[i++] >> 14;
    var m = xh * l + h * xl;
    l = xl * l + ((m & 0x3fff) << 14) + w[j] + c;
    c = (l >> 28) + (m >> 14) + xh * h;
    w[j++] = l & 0xfffffff;
  }
  return c;
}
if (j_lm && navigator.appName == "Microsoft Internet Explorer") {
  BigInteger.prototype.am = am2;
  dbits = 30;
} else if (j_lm && navigator.appName != "Netscape") {
  BigInteger.prototype.am = am1;
  dbits = 26;
} else {
  // Mozilla/Netscape seems to prefer am3
  BigInteger.prototype.am = am3;
  dbits = 28;
}

BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = (1 << dbits) - 1;
BigInteger.prototype.DV = 1 << dbits;

var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2, BI_FP);
BigInteger.prototype.F1 = BI_FP - dbits;
BigInteger.prototype.F2 = 2 * dbits - BI_FP;

// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = new Array();
var rr, vv;
rr = "0".charCodeAt(0);
for (vv = 0; vv <= 9; ++vv) {
  BI_RC[rr++] = vv;
}rr = "a".charCodeAt(0);
for (vv = 10; vv < 36; ++vv) {
  BI_RC[rr++] = vv;
}rr = "A".charCodeAt(0);
for (vv = 10; vv < 36; ++vv) {
  BI_RC[rr++] = vv;
}function int2char(n) {
  return BI_RM.charAt(n);
}
function intAt(s, i) {
  var c = BI_RC[s.charCodeAt(i)];
  return c == null ? -1 : c;
}

// (protected) copy this to r
function bnpCopyTo(r) {
  for (var i = this.t - 1; i >= 0; --i) {
    r[i] = this[i];
  }r.t = this.t;
  r.s = this.s;
}

// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
  this.t = 1;
  this.s = x < 0 ? -1 : 0;
  if (x > 0) this[0] = x;else if (x < -1) this[0] = x + DV;else this.t = 0;
}

// return bigint initialized to value
function nbv(i) {
  var r = nbi();r.fromInt(i);return r;
}

// (protected) set from string and radix
function bnpFromString(s, b) {
  var k;
  if (b == 16) k = 4;else if (b == 8) k = 3;else if (b == 256) k = 8; // byte array
  else if (b == 2) k = 1;else if (b == 32) k = 5;else if (b == 4) k = 2;else {
      this.fromRadix(s, b);return;
    }
  this.t = 0;
  this.s = 0;
  var i = s.length,
      mi = false,
      sh = 0;
  while (--i >= 0) {
    var x = k == 8 ? s[i] & 0xff : intAt(s, i);
    if (x < 0) {
      if (s.charAt(i) == "-") mi = true;
      continue;
    }
    mi = false;
    if (sh == 0) this[this.t++] = x;else if (sh + k > this.DB) {
      this[this.t - 1] |= (x & (1 << this.DB - sh) - 1) << sh;
      this[this.t++] = x >> this.DB - sh;
    } else this[this.t - 1] |= x << sh;
    sh += k;
    if (sh >= this.DB) sh -= this.DB;
  }
  if (k == 8 && (s[0] & 0x80) != 0) {
    this.s = -1;
    if (sh > 0) this[this.t - 1] |= (1 << this.DB - sh) - 1 << sh;
  }
  this.clamp();
  if (mi) BigInteger.ZERO.subTo(this, this);
}

// (protected) clamp off excess high words
function bnpClamp() {
  var c = this.s & this.DM;
  while (this.t > 0 && this[this.t - 1] == c) {
    --this.t;
  }
}

// (public) return string representation in given radix
function bnToString(b) {
  if (this.s < 0) return "-" + this.negate().toString(b);
  var k;
  if (b == 16) k = 4;else if (b == 8) k = 3;else if (b == 2) k = 1;else if (b == 32) k = 5;else if (b == 4) k = 2;else return this.toRadix(b);
  var km = (1 << k) - 1,
      d,
      m = false,
      r = "",
      i = this.t;
  var p = this.DB - i * this.DB % k;
  if (i-- > 0) {
    if (p < this.DB && (d = this[i] >> p) > 0) {
      m = true;r = int2char(d);
    }
    while (i >= 0) {
      if (p < k) {
        d = (this[i] & (1 << p) - 1) << k - p;
        d |= this[--i] >> (p += this.DB - k);
      } else {
        d = this[i] >> (p -= k) & km;
        if (p <= 0) {
          p += this.DB;--i;
        }
      }
      if (d > 0) m = true;
      if (m) r += int2char(d);
    }
  }
  return m ? r : "0";
}

// (public) -this
function bnNegate() {
  var r = nbi();BigInteger.ZERO.subTo(this, r);return r;
}

// (public) |this|
function bnAbs() {
  return this.s < 0 ? this.negate() : this;
}

// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
  var r = this.s - a.s;
  if (r != 0) return r;
  var i = this.t;
  r = i - a.t;
  if (r != 0) return r;
  while (--i >= 0) {
    if ((r = this[i] - a[i]) != 0) return r;
  }return 0;
}

// returns bit length of the integer x
function nbits(x) {
  var r = 1,
      t;
  if ((t = x >>> 16) != 0) {
    x = t;r += 16;
  }
  if ((t = x >> 8) != 0) {
    x = t;r += 8;
  }
  if ((t = x >> 4) != 0) {
    x = t;r += 4;
  }
  if ((t = x >> 2) != 0) {
    x = t;r += 2;
  }
  if ((t = x >> 1) != 0) {
    x = t;r += 1;
  }
  return r;
}

// (public) return the number of bits in "this"
function bnBitLength() {
  if (this.t <= 0) return 0;
  return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ this.s & this.DM);
}

// (protected) r = this << n*DB
function bnpDLShiftTo(n, r) {
  var i;
  for (i = this.t - 1; i >= 0; --i) {
    r[i + n] = this[i];
  }for (i = n - 1; i >= 0; --i) {
    r[i] = 0;
  }r.t = this.t + n;
  r.s = this.s;
}

// (protected) r = this >> n*DB
function bnpDRShiftTo(n, r) {
  for (var i = n; i < this.t; ++i) {
    r[i - n] = this[i];
  }r.t = Math.max(this.t - n, 0);
  r.s = this.s;
}

// (protected) r = this << n
function bnpLShiftTo(n, r) {
  var bs = n % this.DB;
  var cbs = this.DB - bs;
  var bm = (1 << cbs) - 1;
  var ds = Math.floor(n / this.DB),
      c = this.s << bs & this.DM,
      i;
  for (i = this.t - 1; i >= 0; --i) {
    r[i + ds + 1] = this[i] >> cbs | c;
    c = (this[i] & bm) << bs;
  }
  for (i = ds - 1; i >= 0; --i) {
    r[i] = 0;
  }r[ds] = c;
  r.t = this.t + ds + 1;
  r.s = this.s;
  r.clamp();
}

// (protected) r = this >> n
function bnpRShiftTo(n, r) {
  r.s = this.s;
  var ds = Math.floor(n / this.DB);
  if (ds >= this.t) {
    r.t = 0;return;
  }
  var bs = n % this.DB;
  var cbs = this.DB - bs;
  var bm = (1 << bs) - 1;
  r[0] = this[ds] >> bs;
  for (var i = ds + 1; i < this.t; ++i) {
    r[i - ds - 1] |= (this[i] & bm) << cbs;
    r[i - ds] = this[i] >> bs;
  }
  if (bs > 0) r[this.t - ds - 1] |= (this.s & bm) << cbs;
  r.t = this.t - ds;
  r.clamp();
}

// (protected) r = this - a
function bnpSubTo(a, r) {
  var i = 0,
      c = 0,
      m = Math.min(a.t, this.t);
  while (i < m) {
    c += this[i] - a[i];
    r[i++] = c & this.DM;
    c >>= this.DB;
  }
  if (a.t < this.t) {
    c -= a.s;
    while (i < this.t) {
      c += this[i];
      r[i++] = c & this.DM;
      c >>= this.DB;
    }
    c += this.s;
  } else {
    c += this.s;
    while (i < a.t) {
      c -= a[i];
      r[i++] = c & this.DM;
      c >>= this.DB;
    }
    c -= a.s;
  }
  r.s = c < 0 ? -1 : 0;
  if (c < -1) r[i++] = this.DV + c;else if (c > 0) r[i++] = c;
  r.t = i;
  r.clamp();
}

// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a, r) {
  var x = this.abs(),
      y = a.abs();
  var i = x.t;
  r.t = i + y.t;
  while (--i >= 0) {
    r[i] = 0;
  }for (i = 0; i < y.t; ++i) {
    r[i + x.t] = x.am(0, y[i], r, i, 0, x.t);
  }r.s = 0;
  r.clamp();
  if (this.s != a.s) BigInteger.ZERO.subTo(r, r);
}

// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
  var x = this.abs();
  var i = r.t = 2 * x.t;
  while (--i >= 0) {
    r[i] = 0;
  }for (i = 0; i < x.t - 1; ++i) {
    var c = x.am(i, x[i], r, 2 * i, 0, 1);
    if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) {
      r[i + x.t] -= x.DV;
      r[i + x.t + 1] = 1;
    }
  }
  if (r.t > 0) r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1);
  r.s = 0;
  r.clamp();
}

// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m.  q or r may be null.
function bnpDivRemTo(m, q, r) {
  var pm = m.abs();
  if (pm.t <= 0) return;
  var pt = this.abs();
  if (pt.t < pm.t) {
    if (q != null) q.fromInt(0);
    if (r != null) this.copyTo(r);
    return;
  }
  if (r == null) r = nbi();
  var y = nbi(),
      ts = this.s,
      ms = m.s;
  var nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus
  if (nsh > 0) {
    pm.lShiftTo(nsh, y);pt.lShiftTo(nsh, r);
  } else {
    pm.copyTo(y);pt.copyTo(r);
  }
  var ys = y.t;
  var y0 = y[ys - 1];
  if (y0 == 0) return;
  var yt = y0 * (1 << this.F1) + (ys > 1 ? y[ys - 2] >> this.F2 : 0);
  var d1 = this.FV / yt,
      d2 = (1 << this.F1) / yt,
      e = 1 << this.F2;
  var i = r.t,
      j = i - ys,
      t = q == null ? nbi() : q;
  y.dlShiftTo(j, t);
  if (r.compareTo(t) >= 0) {
    r[r.t++] = 1;
    r.subTo(t, r);
  }
  BigInteger.ONE.dlShiftTo(ys, t);
  t.subTo(y, y); // "negative" y so we can replace sub with am later
  while (y.t < ys) {
    y[y.t++] = 0;
  }while (--j >= 0) {
    // Estimate quotient digit
    var qd = r[--i] == y0 ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2);
    if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) {
      // Try it out
      y.dlShiftTo(j, t);
      r.subTo(t, r);
      while (r[i] < --qd) {
        r.subTo(t, r);
      }
    }
  }
  if (q != null) {
    r.drShiftTo(ys, q);
    if (ts != ms) BigInteger.ZERO.subTo(q, q);
  }
  r.t = ys;
  r.clamp();
  if (nsh > 0) r.rShiftTo(nsh, r); // Denormalize remainder
  if (ts < 0) BigInteger.ZERO.subTo(r, r);
}

// (public) this mod a
function bnMod(a) {
  var r = nbi();
  this.abs().divRemTo(a, null, r);
  if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r, r);
  return r;
}

// Modular reduction using "classic" algorithm
function Classic(m) {
  this.m = m;
}
function cConvert(x) {
  if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);else return x;
}
function cRevert(x) {
  return x;
}
function cReduce(x) {
  x.divRemTo(this.m, null, x);
}
function cMulTo(x, y, r) {
  x.multiplyTo(y, r);this.reduce(r);
}
function cSqrTo(x, r) {
  x.squareTo(r);this.reduce(r);
}

Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;

// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
//         xy == 1 (mod m)
//         xy =  1+km
//   xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
  if (this.t < 1) return 0;
  var x = this[0];
  if ((x & 1) == 0) return 0;
  var y = x & 3; // y == 1/x mod 2^2
  y = y * (2 - (x & 0xf) * y) & 0xf; // y == 1/x mod 2^4
  y = y * (2 - (x & 0xff) * y) & 0xff; // y == 1/x mod 2^8
  y = y * (2 - ((x & 0xffff) * y & 0xffff)) & 0xffff; // y == 1/x mod 2^16
  // last step - calculate inverse mod DV directly;
  // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
  y = y * (2 - x * y % this.DV) % this.DV; // y == 1/x mod 2^dbits
  // we really want the negative inverse, and -DV < y < DV
  return y > 0 ? this.DV - y : -y;
}

// Montgomery reduction
function Montgomery(m) {
  this.m = m;
  this.mp = m.invDigit();
  this.mpl = this.mp & 0x7fff;
  this.mph = this.mp >> 15;
  this.um = (1 << m.DB - 15) - 1;
  this.mt2 = 2 * m.t;
}

// xR mod m
function montConvert(x) {
  var r = nbi();
  x.abs().dlShiftTo(this.m.t, r);
  r.divRemTo(this.m, null, r);
  if (x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r, r);
  return r;
}

// x/R mod m
function montRevert(x) {
  var r = nbi();
  x.copyTo(r);
  this.reduce(r);
  return r;
}

// x = x/R mod m (HAC 14.32)
function montReduce(x) {
  while (x.t <= this.mt2) {
    // pad x so am has enough room later
    x[x.t++] = 0;
  }for (var i = 0; i < this.m.t; ++i) {
    // faster way of calculating u0 = x[i]*mp mod DV
    var j = x[i] & 0x7fff;
    var u0 = j * this.mpl + ((j * this.mph + (x[i] >> 15) * this.mpl & this.um) << 15) & x.DM;
    // use am to combine the multiply-shift-add into one call
    j = i + this.m.t;
    x[j] += this.m.am(0, u0, x, i, 0, this.m.t);
    // propagate carry
    while (x[j] >= x.DV) {
      x[j] -= x.DV;x[++j]++;
    }
  }
  x.clamp();
  x.drShiftTo(this.m.t, x);
  if (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
}

// r = "x^2/R mod m"; x != r
function montSqrTo(x, r) {
  x.squareTo(r);this.reduce(r);
}

// r = "xy/R mod m"; x,y != r
function montMulTo(x, y, r) {
  x.multiplyTo(y, r);this.reduce(r);
}

Montgomery.prototype.convert = montConvert;
Montgomery.prototype.revert = montRevert;
Montgomery.prototype.reduce = montReduce;
Montgomery.prototype.mulTo = montMulTo;
Montgomery.prototype.sqrTo = montSqrTo;

// (protected) true iff this is even
function bnpIsEven() {
  return (this.t > 0 ? this[0] & 1 : this.s) == 0;
}

// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e, z) {
  if (e > 0xffffffff || e < 1) return BigInteger.ONE;
  var r = nbi(),
      r2 = nbi(),
      g = z.convert(this),
      i = nbits(e) - 1;
  g.copyTo(r);
  while (--i >= 0) {
    z.sqrTo(r, r2);
    if ((e & 1 << i) > 0) z.mulTo(r2, g, r);else {
      var t = r;r = r2;r2 = t;
    }
  }
  return z.revert(r);
}

// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e, m) {
  var z;
  if (e < 256 || m.isEven()) z = new Classic(m);else z = new Montgomery(m);
  return this.exp(e, z);
}

// protected
BigInteger.prototype.copyTo = bnpCopyTo;
BigInteger.prototype.fromInt = bnpFromInt;
BigInteger.prototype.fromString = bnpFromString;
BigInteger.prototype.clamp = bnpClamp;
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
BigInteger.prototype.lShiftTo = bnpLShiftTo;
BigInteger.prototype.rShiftTo = bnpRShiftTo;
BigInteger.prototype.subTo = bnpSubTo;
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
BigInteger.prototype.squareTo = bnpSquareTo;
BigInteger.prototype.divRemTo = bnpDivRemTo;
BigInteger.prototype.invDigit = bnpInvDigit;
BigInteger.prototype.isEven = bnpIsEven;
BigInteger.prototype.exp = bnpExp;

// public
BigInteger.prototype.toString = bnToString;
BigInteger.prototype.negate = bnNegate;
BigInteger.prototype.abs = bnAbs;
BigInteger.prototype.compareTo = bnCompareTo;
BigInteger.prototype.bitLength = bnBitLength;
BigInteger.prototype.mod = bnMod;
BigInteger.prototype.modPowInt = bnModPowInt;

// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);